"Singlebarrelled names for doubleparalleled twixtytwins."

(286.3-288.4)  After yesterday's reading covering fatherhood, the fall, and chaos, we see that it's a sort of universal truth that HCE's fate was to be determined by a random shuffling of a deck that prompts a type of cosmic game of cards.  With the first card dealt, the narrator asks us to turn it over to see what we've got.

We now uncover the first problem posed on this particular evening to the geometrically-challenged Kevin:  construct an equilateral triangle, or an "aquilittoral dryankle" (or a river delta, indicating ALP, who is symbolized by the river, the triangle, and the Greek letter Delta).  Kevin begins his work with a sort of parody of the Sign of the Cross.  His brother, Dolph (the Shem to Shaun's Kevin in this passage), asks Kevin if he knows how to solve the problem.  Kevin says he can't, and asks Dolph whether he can.  Kevin is "expecting the answer guess," indicating that he both anticipates that Dolph knows the answer (meaning that "guess" equals "yes") and that Dolph won't tell him either way.  Kevin then asks Dolph/Shem (here, for the moment, "Sem") to tell him the answer.

Instead of getting a straightforward answer, Dolph gives a complicated and extended geometry lesson, which Tindall calls in his Reader's Guide "the heart of this chapter."  Dolph begins by instructing, "First mull a mugfull of mud, son."  As McHugh notes, this means Dolph is telling Kevin to start at the beginning, and think about the mud from which Adam, the first man, was formed.  Emphasizing this a few lines later, Dolph tells Kevin to "take your mut for a first beginning, big to bog, back to bach," or, in other words, to consider his mother the first beginning, and to move from the big ideas to the primordial bog, or back to the brook (which is the English translation of the German "bach").  Moving on, Dolph says that in order to get "a locus for alp" Kevin must "get a howlth on her bayrings," which in a sense means to get a hold of our ever-present Howth Castle or Howth Hill for her bearings.  Dolph says to mark the Isle of Man as "a" or "alpha" on the map.  With this done, he considers everything to be in "applepine odrer," or in accordance with the state of human existence in Eden, under the appletree.

Now the geometry lesson is interrupted by an extended parenthetical aside, which serves as a clue to both the relationship between Kevin/Shaun and Dolph/Shem and the problem of the equilateral triangle/ALP.  In keeping with previous depictions of Shem, Dolph is described as "dean of idlers."  A long passage in Latin -- which asks us to turn our minds toward Bruno and Vico and recognize that the river (ALP) is the predominant force and is embraced by the rival forces (Shem and Shaun) on either side of its banks -- then interrupts this parenthetical.  Returning to the parenthetical, today's reading ends with a quick summary of Dolph's scholastic life, in which he taught pupils and engaged in a variety of underhanded scholarly practices, such as forging letters and telling doublecrossing lies.  

We're just at the beginning of a couple of days' journey into this parenthetical, so more to come on this tomorrow . . . .